Toppers Notes on Real Valued Functions (Functions)

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Table of Content

  • Definition of a function.
  • Vertical line test.
  • The number of functions.
  • Value of a function.
  • Domain, Co-domain, and Range.
  • Intervals.
  • Algebra of functions (scalar multiplication, addition, subtraction, multiplication, division).
  • Important Definitions (variables, constants, equal functions).
  • Definition of real valued functions.
  • One one or injective functions.
  • Many one functions.
  • Onto or surjective functions.
  • Into functions.
  • Bijective functions.
  • Types of functions (constant function, identity function, absolute value function (modulus function), signum function, greatest integer function, fraction part function, least integer function, algebraic functions, reciprocal function, transcendental functions, exponential functions, logarithmic functions, power functions).
  • Even and Odd functions.
  • Periodic functions.
  • Composite functions.
  • The inverse of a function.